Problem: Michael is 20 years older than William. Michael and William first met 3 years ago. Seventeen years ago, Michael was 3 times as old as William. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and William. Let Michael's current age be $m$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $m = w + 20$ Seventeen years ago, Michael was $m - 17$ years old, and William was $w - 17$ years old. The information in the second sentence can be expressed in the following equation: $m - 17 = 3(w - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = m - 20$ . Substituting this into our second equation, we get the equation: $m - 17 = 3($ $(m - 20)$ $ -$ $ 17)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 17 = 3m - 111$ Solving for $m$ , we get: $2 m = 94$ $m = 47$.